Math Olympiad Question with

Denis from ‪@ThePhysicsMathsWizard‬ challenges me with a question from the Vietnam Math Olympiad about the floor function... #tomrocksmaths #thephysicsmathswizard
The question asks for all positive solutions to the equation 0.9t = floor(t) / (t - floor(t)). My approach was to first rule out integer solutions and then solve for t in the range (n, n+1). This leads to a quadratic equation and a series of inequalities that need to be satisfied for the solutions to be valid.
Check out Denis's channel ‪@ThePhysicsMathsWizard‬ here: / thephysicsmathswizard
Produced by Dr Tom Crawford at the University of Oxford. Tom is an Early-Career Teaching and Outreach Fellow at St Edmund Hall: www.seh.ox.ac.uk/people/tom-c...
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[@TomRocksMaths]

For more collabs with Tom check out the designated playlist here: kzbin.info/aero/PLMCRxGutHqflwDzFFt33UwO8ncqg4GEZj

[@ThePhysicsMathsWizard]

Great job Tom, am glad for working with you on this one, I like the way you solved the problem and the thought process. Cheers

[@TomRocksMaths]

Thanks for joining Denis!!

[@leif1075]

@@TomRocksMaths Thanks for sharing. I hope you can respond to my other comment when you can. Thanks very much.

[@Triskelion345]

Thanks 😁

[@susie7301]

Wow, I wasn't expecting to find a maths video so interesting! It'd be really cool if you could do some videos on similar questions, and how you can practise to improve your problem solving skills! I'm an alevel (further) maths student and although I find the class content fine, I struggle with things like the senior maths challenge as I just can't think straight to a solution haha

[@boualemhabib9949]

Humility is so intrinsic to your nature that I truly believe that many people didn't think that you already knew the solution to the equation as soon as it was within your eyesight. I have followed you on youtube for a while. I enjoyed your 125 miles self inflicted torture run. As the french would say, de la folie pure.Tout mon respect. you are a true teacher. Chapeau.

[@TomRocksMaths]

[@maxime863]

Great video Dr. Tom

[@eggtimer2]

Very well done. It is inspiring!

[@prismblack5003]

You guys are Brilliant 👌🏾

[@abbe23456789]

Great video! Make more videos like this, were you try to solve problems live. It's really interesting.

[@shivashankar28]

Amazing prof, haven't learnt this as an undergraduate in Electrical Engineering, but pretty cool !

[@husseinmohamud6506]

How hard is eee at university?

[@m.moonsie]

@@husseinmohamud6506 very. black magic

[@domc3743]

I love how everything follows logically (i.e no magic tricks) really great stuff Tom

[@TomRocksMaths]

thanks - glad you enjoyed it!

[@phenixorbitall3917]

Great :) It is a cool mixture of nerdyness and useful entertainment. Watching both of you doing maths feels like listening to two musicians embarking on some intense jazzy maths improvisation - pretty cool. It made me smile at the end :) Please continue collaborating together!

[@TomRocksMaths]

Glad you enjoyed it!

[@babagaming4943]

Woooo this collaboration was nice the number is so cool. I knew this channel from math physics wizard but their is also good content. Yap guys keep on keeping on

[@nuranichandra2177]

Admire the fantastic problem and solution strategy

[@floreaciprian9742]

These videos are so much fun to watch. We get to meet other youtubers passionate about maths, we see both sides challanged, we see the thought process both. This idea to involve other people was just brilliant. Thanks and i hope we get to see more

[@TomRocksMaths]

plenty more collabs coming in 2022 :)

[@floreaciprian9742]

@@TomRocksMaths great news. Happy new year mate

[@eugeneyong6674]

Amazing!

[@Twister15X]

I've done it in the same way hahaha, the only diference is that a called t = n + e, where n is an integer and 'e' is a numbem between 0 and 1. So in the end what changed was the condition that would filter the values of n.

[@CommanderdMtllca]

Do more like this!!! I love seeing math videos where someone has to think out loud instead of guiding the video with a scripted solution.

[@RobertSmith0008]

Moreover, to see why the first t doesnt work, it is easy to see from the expression (with negative radical) that t < n/2, which contradicts the fact that t >n

[@antooshon4904]

awesome man

[@desertstorm6927]

I like how doctor aproaches every problem. Also i like how innocent this guy looks. wow 🥰

[@tanpham762]

Maths is always interesting!

[@iteerrex8166]

Seemingly simple but a tricky little problem. Nicely done professor.

[@TomRocksMaths]

Many thanks!

[@asd-bl5ur]

An alternate solution could be forming a quadratic in fractional part of t, and then using the concept of location of roots to figure out the answer

[@parkie8167]

God this was such a fun problem. Gonna go look at the vietnamese math olympiad lmao

[@strafehelix]

It'll be interesting to see you do a engineering exam, it's based upon maths, mechanical which is beams and All and electrical

[@rehab3398]

Never seen a mathematician with the drip that this man has

[@TomRocksMaths]

[@RC32Smiths01]

Amazing as always, Tom!

[@TomRocksMaths]

Thank you! Cheers!

[@NateCrownwell]

Really cool math problem :)

[@nDreaw12]

Damn I feel so dumb by this Video but still love it and appreciate all ur Vids Tom 👌

[@aashsyed1277]

I watch that channel!!!!

[@RobertSmith0008]

you can show immediately that n is less than 9 as follows,: From the equation you get that t - n = n / (0.9 t) which should be less than 1, This implies that 10n < 9t. But t

[@TomRocksMaths]

nice!

[@zarifahmed8549]

You should make a video to advice students about A levels and GCSEs

[@TomRocksMaths]

I discuss this a lot in my 50k Q&A video here: kzbin.info/www/bejne/aIDZnY2uqcp4aNk

[@ashugoshu]

I was that kid who always sleep when hearing about equations but I'm finding it more interesting RN . Well I've been watching Tom's content for over a year I like his contents and he is cute as always 😙

[@TomRocksMaths]

amazing, keep at it and you'll be a maths fan in no time!

[@GreenMeansGOF]

I think it’s important to note that up until the smiley face, n could have been 0. I don’t think you noticed that that case got eliminated.

[@rijulbarot2195]

Hey, I found a method free of the quadratic complications, so I thought id share it. Write the greatest integer t to be x, and then t - x = f, ( f for fraction :D and it goes from (0,1)) , so the equation becomes 0.9(x+f) = x/f, which implies 0.9(x+f) > x , so x < 9f and from the range of f we get the possible values of x to be 1,2,3,4,5,6,7,8. Cheers and great video btw!

[@DmitDmit1]

I've solved it the same way. But I find his solution is more straightforward. And you still have to express f in terms of x, can't avoid dealing with quadratic here.

[@TomRocksMaths]

nice!

[@sumitprabhakar177]

After you get 0.9t = floor(t)/integer part (t) then it can be easily analyzed graphically

[@chad_the_stud]

analytical thinking, problem solving skills are valid if you know the details of the topic

[@robinrahman8623]

I hope everyone else's face lit up the way mine did when you were close to finding the solution .o.

[@xamael1989]

Lovely

[@natural-926]

Tom, you are the best and coolest Math Professor in the World

[@TomRocksMaths]

[@eliascabrera5539]

Thats Ninja

[@JanxakaJX]

You made this really fun Tom. Thanks for making maths fun :) Also, really impressed by how well you did this question and your reasoning

[@TomRocksMaths]

Thanks! 😃

[@dave_thebrave]

at 13:15 aw math is gonna be very interesting to see how much work this guy

[@ekisvioleolivaradamos6701]

amazing....

[@TomRocksMaths]

Thanks a lot 😊

[@gametimewitharyan6665]

I am so happy to solve this question myself, even though I don't prepare for Olympiads and I am sooo much happy because I am only in class 10th 🥳🥳🥳

[@vansf3433]

Why do you guys like High school or SE maths?

[@helloitsme7553]

I first thought it said 0 times 9 and I was like what is this a prank

[@gordonmacgregor7668]

me sitting pretending like I have any clue wtf is going on

[@naveenwanigasundara2206]

cool pro

[@Kimm4321]

I'm sorry Tom my girfrend unliked this video but dont worry I undisliked and liked your video. Keep it up super awesome!

[@kojoabiam7688]

Awesome!👍🎄 I follow you from Ghana. Please adjust your light, there seems to be a glare on the board. Thanks

[@TomRocksMaths]

Thanks for the tip!

[@weonlygoupfromhere7369]

Man has a massive noggin. I don't even know where to start

[@michaelanderson7715]

up, obviously

[@sztojanbarna]

I understand math until it doesn't contain letters!

[@2sdd]

dude seems like a good teacher but i cant focus cuz he looks like a clown

[@boualemhabib9949]

it takes a clown to spot another., however, you sir, are the exception to the rule. Enough said ///.